Applications of Mathematics

, Volume 54, Issue 1, pp 79–85 | Cite as

New results on periodic solutions for a kind of Rayleigh equation

Article

Abstract

The paper deals with the existence of periodic solutions for a kind of non-autonomous time-delay Rayleigh equation. With the continuation theorem of the coincidence degree and a priori estimates, some new results on the existence of periodic solutions for this kind of Rayleigh equation are established.

Keywords

Rayleigh equations existence periodic solution a priori estimate 

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References

  1. [1]
    F. D. Chen: Existence and uniqueness of almost periodic solutions for forced Rayleigh equations. Ann. Differ. Equations 17 (2001), 1–9.Google Scholar
  2. [2]
    F. D. Chen, X. X. Chen, F. X. Lin, J. L. Shi: Periodic solution and global attractivity of a class of differential equations with delays. Acta Math. Appl. Sin. 28 (2005), 55–64. (In Chinese.)MathSciNetGoogle Scholar
  3. [3]
    K. Deimling: Nonlinear Functional Analysis. Springer, Berlin, 1985.MATHGoogle Scholar
  4. [4]
    R. E. Gaines, J. L. Mawhin: Coincidence Degree, and Nonlinear Differential Equations. Lecture Notes in Mathematics, Vol. 568. Springer, Berlin, 1977.MATHGoogle Scholar
  5. [5]
    C. Huang, Y. He, L. Huang, W. Tan: New results on the periodic solutions for a kind of Reyleigh equation with two deviating arguments. Math. Comput. Modelling 46 (2007), 604–611.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    F. Liu: On the existence of the periodic solutions of Rayleigh equation. Acta Math. Sin. 37 (1994), 639–644. (In Chinese.)MATHGoogle Scholar
  7. [7]
    S. P. Lu, W. G. Ge: Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear Anal., Theory Methods Appl. 56 (2004), 501–514.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    S. P. Lu, W. G. Ge, Z. X. Zheng: Periodic solutions for a kind of Rayleigh equation with a deviating argument. Appl. Math. Lett. 17 (2004), 443–449.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    S. P. Lu, W. G. Ge, Z. X. Zheng: Periodic solutions for a kind of Rayleigh equation with a deviating argument. Acta Math. Sin. 47 (2004), 299–304.MATHMathSciNetGoogle Scholar
  10. [10]
    L. Peng: Periodic solutions for a kind of Rayleigh equation with two deviating arguments. J. Franklin Inst. 7 (2006), 676–687.CrossRefGoogle Scholar
  11. [11]
    G.-Q. Wang, S. S. Cheng: A priori bounds for periodic solutions of a delay Rayleigh equation. Appl. Math. Lett. 12 (1999), 41–44.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    G.-Q. Wang, J. R. Yan: Existence theorem of periodic positive solutions for the Rayleigh equation of retarded type. Portugal. Math. 57 (2000), 153–160.MATHMathSciNetGoogle Scholar
  13. [13]
    G.-Q. Wang, J. R. Yan: On existence of periodic solutions of the Rayleigh equation of retarded type. Int. J. Math. Math. Sci. 23 (2000), 65–68.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    Y. Zhou, X. Tang: On existence of periodic solutions of Rayleigh equation of retarded type. J. Comput. Appl. Math. 203 (2007), 1–5.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.School of Mathematical Science and Computing TechnologyCentral South UniversityChangsha, HunanP.R.China
  2. 2.School of Materials Science and EngineeringCentral South UniversityChangsha, HunanP.R.China

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